Below is a detailed list of topics covered in CS 688 in 2022. The
actual topics covered this will be similar but may change. References to
outside materials (MLPP, PGM, Domke) refer to the resources listed on
the main page.
Introduction
- Course Intro ([MLPP] Ch 1 or [PGM] p. 1-12)
- Random variables and joint distributions ([MLPP] p. 27-30 or [PGM]
19-22)
- Slide sources: Domke
Lecture 1
- Probability Calculus: Marginalization, Conditioning, Chain Rule,
Bayes’ Rule. ([MLPP] 29-30 or [PGM] p. 21-22)
- Marginal and Conditional Independence ([MLPP] p. 31-32 or [PGM]
p. 23-25)
Bayesian networks
- Bayesian Network Representation ([MLPP] p. 309-330 or [PGM]
p. 51-63)
- See also Domke
Lecture 1 and Lecture
2
- Bayes net Markov Properties ([PGM] 69-76)
- The Bayes Ball algorithm
- Using independence to simplify queries
- KL Divergence ([PGM] 699, [MLPP] 58)
- The Likelihood Function ([PGM] 719, [MLPP] 69)
- Maximum Likelihood Learning ([PGM] 719-722, [MLPP] 71)
- Bernoulli Example ([PGM] 718-719)
- The standard parameterization for discrete Bayesian networks. ([PGM]
p. 725-726)
- The decomposition of the likelihood function over the network.
([PGM] p. 723-725)
- Maximum likelihood estimation for individual CPTs. ([PGM]
p. 726)
Markov networks
- Undirected graphs and factors ([PGM] p. 103-104, 106-108, [MLPP]
663-669)
- Joint distribution and partition function ([PGM] p. 105, 108, [MLPP]
same as previous)
- Gibbs distribution ([PGM] p. 108, [MLPP] 667-668)
- Markov properties ([PGM] p. 114-120, [MLPP] 664)
- Ising Model ([PGM] p. 124-127, [MLPP] 670)
- Conditional random fields
- Bayesian networks as Markov networks. ([PGM] 134-137, [MLPP]
664)
- Conditioning and the factor reduction algorithm ([PGM] 110-112)
- Efficient factor product sums ([PGM] 296)
- Variable elimination examples for chains and trees ([PGM] 292-296,
[MLPP] 709- 712)
- Domke notes on Message Passing: Lecture
9, Lecture
10
- Exponential Families: Domke Lecture
11 and Lecture
12 notes
- Conditional and Hidden Exponential Families: Domke notes 12
and 13
- Asymptotic distribution of maximum-likelihood estimator and
Cramer-Rao bound: Domke notes 14
and 15
Markov chain Monte Carlo and Bayesian Inference
- Markov chain definition ([PGM] 507, [MLPP] 591)
- State sequences and sampling ([PGM] 508)
- The t-step distribution ([PGM] 508)
- Convergence and the stationary distribution ([PGM] 508-511, [MLPP]
598-206)
- See also Domke Lecture
15 and Lecture
16
- Limiting distributions
- Stationary distributions
- Detailed Balance [PGM 515-516]
- Designing Markov chains for a distribution P(X) ([PGM] 511-512)
- Proof of convergence of the Gibbs sampler to P(X) ([PGM]
512-514)
- The Metropolis Hastings Algorithm ([PGM] 514-518, [MLPP]
850-851)
- Demo of the random-walk Metropolis Hastings sampler
- Heuristics for assessing convergence
- Autocorrelation analysis
- Hamiltonian Monte Carlo
- Reading: Sections 5.1–5.3 of “MCMC Using Hamiltonian Dynamics” by
Radford Neal
- Bayes rule as updating beliefs in light of evidence ([PGM] 738)
- Application of Bayesian inference to learning ([PGM] 737-741)
- Bayesian inference and the Beta/Bernoulli model ([PGM] 733-737)
Variational inference
Probabilistic programming